Flows (matching labor flows in search models with labor force participation)

Flows between the three states determine the rates of unemployment, employ­ment, and inactivity. These flows are determined by the arrival rates and separation rates in the model, as well as the transition ofworkers across types. Table 2.1 displays the mapping of components of the search model to each flow

1. Consider the flow from Unemployment (U) and Inactivity (N) to Employment (E), henceforth the UE and N E rates. The matching probability of workers in U or N is A_i = s_ip(ỡ). The difference in the matching probability of nonpartic­ipants and unemployed agents comes from the fact that su > sn , reflecting that high search cost types have a lower chance of reaching the labor market than low search cost types, who are unemployed.
2. The UU, UN, NU , and NN flows for agents result from the probabilities of remaining non-employed and the transition matrix over types, X. Note that for an agent in U , they can either move to E or N , or stay in U. We discussed the UE flow above. With probability 1 — A_i the agent stays without a job. The agent’s choice of search effort depends on the agent’s type. If the agent’s type changes, the agent will move between U and N the next period. The transition probability over agents’ types affects the movement of agents between U and N in this way.
3. The EU and EN flows of workers from employment to unemployment and out of the labor force are determined by the separation probability Ỏ of the worker. In this case with no aggregate uncertainty, it is innocuous to assume that separations are constant and exogenous at rate s. The exogenous sepa­ration probability Ỏ causes all workers to separate into non-employment at the same rate. The distribution of search cost types in the employment pool dic­tates the relative size of the EU vs. EN flow, while the magnitude of Ỏ dictates the percentage of all employed workers who separate in a given month.